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Question

Two waves having same amplitude (A), wavelength (λ) and frequency (f) are propagating in the same direction. They interfere such that the amplitude of resultant wave is zero. The path difference between two wave can be :

A
λ
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B
2λ
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C
3λ2
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D
3λ4
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Solution

The correct option is C 3λ2
For the two waves having same amplitude, destructive interference results into minimum amplitude for the resultant wave.
Aresultant=|A1A2|
For the given zero resultant amplitude,
Aresultant=|AA|=0
It represents the case of destructive interference.
Hence path difference between waves will be odd multiples of λ2 i.e Δx=λ2, 3λ2, 5λ2,..etc
In a generalised form,
Δx=(2n+1)λ2
Δx=3λ2(for n=1)
Option (c) is correct.

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